[CORE-14466] ts: Fix spillover race

[Lazin]

This PR

• Downgrades error to warning.
• Interrupts housekeeping in case if replication of the archival STM command times out. This is needed to prevent certain race conditions from happening (when the replication times out but the command is replicated and then applied asynchronously).

Backports Required

• none - not a bug fix
• none - this is a backport
• none - issue does not exist in previous branches
• none - papercut/not impactful enough to backport
• v25.2.x
• v25.1.x
• v24.3.x

Release Notes

• none

[Copilot]

Pull Request Overview

This PR addresses race conditions in the spillover handling of the NTP archiver service by downgrading a spillover invariant violation from an error to a warning and adding exception throwing for failed archive operations. The changes help prevent race conditions when replication of archival STM commands times out but are still applied asynchronously.

Key Changes

• Downgrades spillover invariant violation log from error to warning level
• Adds exception throwing for failed archive retention and garbage collection operations
• Improves error handling consistency across archival operations

[vbotbuildovich]

CI test results

test results on build#75314

test_class	test_method	test_arguments	test_kind	job_url	test_status	passed	reason	test_history
LogCompactionTxRemovalTest	test_tx_control_batch_removal	null	integration	https://buildkite.com/redpanda/redpanda/builds/75314#019a3532-fce7-42fb-b9af-aac611c9ed5f	FLAKY	14/21	upstream reliability is '95.38043478260869'. current run reliability is '66.66666666666666'. drift is 28.71377 and the allowed drift is set to 50. The test should PASS	https://redpanda.metabaseapp.com/dashboard/87-tests?tab=142-dt-individual-test-history&test_class=LogCompactionTxRemovalTest&test_method=test_tx_control_batch_removal

[oleiman]

lgtm

[vbotbuildovich]

/backport v25.2.x

[vbotbuildovich]

/backport v25.1.x

[vbotbuildovich]

Failed to create a backport PR to v25.1.x branch. I tried:

git remote add upstream https://github.com/redpanda-data/redpanda.git
git fetch --all
git checkout -b backport-pr-28281-v25.1.x-806 remotes/upstream/v25.1.x
git cherry-pick -x 4e5630a2e0 a6058cc31e c85416a4da

Workflow run logs.